Method and Apparatus for Control of a Synchronous Permanent Magnet Motor, Particularly Over a Long Cable in a Well

ABSTRACT

A synchronous permanent magnet motor is controlled independently of position sensing means by determining the system parameters including the motor impedance and back-emf and the cable impedance and supplying power according to a predefined voltage:frequency ratio which is determined based on said system parameters to provide a desired rate of acceleration determined by the supply voltage.

CROSS-REFERENCE TO RELATED APPLICATIONS

The present application is a continuation of U.S. patent applicationSer. No. 13/811,418, filed Feb. 26, 2013 by Philip Head, et al. andentitled “Method and Apparatus for Control of a Synchronous PermanentMagnet Motor, Particularly Over a Long Cable in a Well,” which is anational phase filing under 35 U.S.C. 371 of International ApplicationNo. PCT/GB2011/051402, filed Jul. 22, 2011, which claims the benefit ofand priority to United Kingdom Patent Application No. 1012321.4, filedJul. 22, 2010, all of these applications are incorporated herein byreference in their entirety.

STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH OR DEVELOPMENT

Not applicable.

REFERENCE TO A MICROFICHE APPENDIX

Not applicable.

BACKGROUND OF THE INVENTION

1. Field of the Invention

This invention relates to the control of synchronous permanent magnetmotors, particularly though not exclusively in a downhole environmentsuch as a hydrocarbon (oil, gas, or mixed oil and gas) well.

2. Description of the Related Art

Permanent magnet motors are anticipated to replace the standardinduction motor in downhole ESP applications. Due to their power densitycompared to current technologies and to their high efficiency due theirbuilt in excitation, it is expected that they will competing more andmore with induction motor based ESP systems.

Brushless permanent magnet motors conventionally comprise a rotor havingpermanent magnets, and a stator winding which induces the rotor to turn.The motor is supplied with current, which is electronically commutatedto energise different parts of the winding as the rotor turns.

Conventional art as exemplified by US 2009/0146592 A1 and JP 2001025282relies upon closed loop control methods to start and operate asynchronous motor. These involve either direct measurements orestimation of control quantities like position from directly measurablequantities like voltages and currents.

In order to control the rotor, the rotor position is determined. Thiscan be a position sensor to coordinate the variable speed drive deviceswitching with the position of the motor back-EMF. This typicallyrequires a Hall effect device based position sensor, a resolver orencoder to provide three signals shifted 120° that are used by thevariable speed drive (VSD) to time the signals to the devices. Due tothe harsh nature of the environment, these position sensors are notreliable and may not survive the prevailing well temperature.Alternatively sensorless algorithms have been developed which deduce therotor position from the motor back emf, which however can be veryunreliable at motor start up and at low speeds if the motor is underload.

A synchronous motor runs at the same speed as the supply frequency toits armature. The actual speed in revolution per minute (rpm) is afunction of supply frequency and the number of pole pairs of the field.Unlike asynchronous motors, synchronous motors require a start-upsequence to ensure that the rotor gains speed without locking. Directon-line starting methods seldom work on synchronous machines. The amountof torque to be generated by the interaction of the field with thearmature current depends on the magnitude of the rotor field and thestator currents. It is the interaction between these fields thatgenerates the torque required to accelerate the rotor and supply thetorque required by the load. Ideally these fields must be in quadrature(90 Electrical Degrees) to maximize the torque generation. So for asuccessful start, the amount of current supplied to the stator has to beadequate and the rate at which the motor is accelerated needs to beconsistent with the torque generated. Conventionally, there are two waysto do this, both being closed-loop methodologies:

(i) A physical position sensor is provided, and maximum torque isensured by maintaining a 90° angular relationship between the rotorfield and armature currents. In ESP applications, the distance of theposition sensor, for example, some 3000 m from the drive is prohibitiveand furthermore the reliability of such systems is reduced by theaddition of additional devices and associated cables.

The position sensor means indicates when the switches and open or closedto supply stator currents, and typically comprises either a Hall effectsensor or a group of optical devices positioned 120° apart. The signalsfrom the three sensors are used to generate the gating signals. In suchsystems, the current level is controlled to set the torque level so thusacceleration.

(ii) Alternative, sensorless methods make use of direct measurements ofvoltage and current and from the voltage equation estimate the positionby integration methods. Such methods are difficult to use in ESPsystems, primarily because of the long cables between the motor and thedrive and the fact that in the majority of cases cable impedances arenon-symmetrical due to the flat configuration of the cable, which istypically supported by strapping it to the production tubing. Thevoltages and current are therefore no longer balanced and thereforeestimation methods are no longer accurate. Position errors thereforelead to lower stability margin of the system and may lead to the motorlosing synch during transients or when there is gas in the well and themotor loses load momentarily.

It is an object of the present invention to provide a more satisfactoryway of controlling a synchronous permanent magnet motor, particularly indownhole applications where the conductors are of great length.

SUMMARY OF THE INVENTION

Accordingly in its various aspects the present invention provides amethod and system as defined in the claims.

In accordance with an embodiment, a method of controlling an electricpower supply to a synchronous permanent magnet motor having a pluralityof windings so as to accelerate the motor through a range of speed fromrest, comprising:

supplying each winding with a root mean square supply voltage V appliedat a supply frequency f via a respective conductor according to theexpression

V=V0+vf_Ratio*f

wherein V0 is an initial constant voltage, vf_Ratio is a constant ratioof voltage over frequency, V0 being sufficient to supply sufficientcurrent to generate the required torque to turn the motor fromstationary, and the vf_Ratio being sufficient to ensure excess torque isavailable during the start-up period and during operation to overcomeany transient load that may be present, and the power supply iscontrolled independently of any rotor position signal.

In accordance with another embodiment, a method of controlling anelectric power supply to a synchronous permanent magnet motor driving aload and having a plurality of windings, each winding being suppliedwith power at a root mean square supply voltage V3 and a supplyfrequency via a respective conductor, so as to accelerate the motorthrough a range of speed from rest, comprising: determining systemparameters including characteristics of the load, the impedance andback-emf of the motor and the impedance of each of the conductors;

determining based on said system parameters a root mean square firstvoltage V0 at which the supply generates torque in the motor at restsufficient to start the motor in rotation;

determining based on said system parameters a ratio between the supplyvoltage V3 and supply frequency, wherein the ratio defines, for each ofa range of supply frequencies corresponding to the range of speed of therotating motor, a root mean square second voltage V2 at which currentflowing through each winding increases with both increase and decreasein voltage, and V2>V0;

supplying power to each winding at the first voltage V0 so as to startthe motor from rest;

and progressively increasing both the supply voltage and the supplyfrequency while maintaining the supply voltage V3 with respect to supplyfrequency at a value sufficiently in excess of V2 to ensure stableoperation of the motor until the motor has reached a desired operatingspeed;

wherein the said ratio between the supply voltage V3 and supplyfrequency is determined based on said system parameters to provide adesired rate of acceleration determined by the supply voltage.

In accordance with another embodiment, a system comprises:

a synchronous permanent magnet motor deployed in a wellbore and drivinga load and having a plurality of windings,

and a control apparatus for supplying each winding with power at a rootmean square supply voltage V3 and a supply frequency via a respectiveconductor,

wherein the control apparatus is configured to supply each winding witha root mean square supply voltage V applied at a supply frequency f viaa respective conductor according to the expression

V=V0+vf_Ratio*f

wherein V0 is an initial constant voltage, vf_Ratio is a constant ratioof voltage over frequency, V0 being sufficient to supply sufficientcurrent to generate the required torque to turn the motor fromstationary, and the vf_Ratio being sufficient to ensure excess torque isavailable during the start-up period and during operation to overcomeany transient load that may be present, and the power supply iscontrolled independently of any rotor position signal.

The motor may be arranged to drive an electric submersible pump,particularly a pump comprising a centrifugal impeller driven by themotor.

The system is particularly advantageous where each conductor is at least50 m in length, still more where each conductor is at least 600 m inlength, yet more where each conductor is at least 3000 m in length.

BRIEF DESCRIPTION OF THE DRAWINGS

Further features and advantages will be apparent from the illustrativeembodiment of the invention which will now be described, purely by wayof example and without limitation to the scope of the claims, and withreference to the accompanying drawings, in which:

FIG. 1A is a side view of a motor disposed in a well and controlled by acontrol system;

FIG. 1B is a diagrammatic view of the motor control system;

FIG. 2 is a graph showing the voltage:frequency (V:f) ratio;

FIG. 3 is a graph showing the motor current:supply voltage (I:V)relationship at one frequency;

FIG. 4 is a graph showing the motor current:supply voltage (I:V)relationship at five frequencies corresponding to the range of speed ofthe motor; and

FIG. 5 is an equivalent circuit diagram representing the motor and cabletogether with an isolation transformer.

DETAILED DESCRIPTION

Referring to FIG. 1A, an electric submersible pump comprises a pump 14powered by an electric motor 13 via a gearbox 16, which is lowered downa cased well 18 on, for example, coiled tubing 15. An electric cable 17extends from the surface to supply the motor with electricity. The pump14 draws well fluid in through an inlet 19 and into the coiled tubing15. In a downhole application such as this, particularly where the motoris powered using a long cable, a brushless DC motor having the followingdescribed control system is ideal. The long cable could alternatively beattached to the casing of the well, so that the ESP mates with anelectrical connector when it reaches the desired destination.

Systems of this type are typically supplied with power from a 3-phase ACsource. The AC voltages are converted to DC by a rectifier that issupported by capacitors to ensure ripple free DC output, also called aDC-Link. It is from this DC-Link that the voltages supplied to the motorare generated, typically by Pulsed Width Modulation (PWM) techniques butalternatively by simpler methods such as six-step or a combination ofPWM and six-step, referred to as a hybrid method.

Referring to FIG. 1B, a microcontroller 10 controls a voltage controlunit 20 and a pulse-width modulation controller unit 30. Power 27 issupplied and rectified in a rectification unit 25, before fed towindings of the stator of the permanent magnet motor 40 by switchingunit 35. The rectification unit also supplies power at the steadyvoltage maintained by the voltage control unit 20, and the switchingunit 35, under the control of the pulse-width modulation controller unit30, supplies a number of windings (not shown) via supply lines 37 sothat the poles (also not shown) of the permanent magnets on the rotorare attracted and/or repelled by the windings so that the rotor iscaused to turn. The pulse-width modulation controller unit 30, andultimately the microprocessor 10 controls the frequency with which thewindings are switched on and off, each winding having the same frequencybut out of phase with the other windings. The microprocessor 10 respondsto an input 12, which may be either an on-off signal for the motor tooperate at a predetermined speed, or a speed at which the motor is torotate.

The motor 40 is a synchronous permanent magnet brushless AC motor whichis electronically commutated (i.e. supplied with an appropriate waveformso as to intermittently excite each of its windings) by insulated gatebipolar transistor switches within the switching unit 35.

The pulse width modulation controller unit 30 provides both frequencyand voltage control by switching the supply so as to provide pulses(e.g. a sinusoidal or square wave supply) to each winding anddetermining the frequency of that supply, and defining the width of theDC pulses so as to define the root mean square voltage.

The voltage control unit 20 operates in a conventional way to ensure aconstant, ripple free DC supply from the rectifier 25 to the switchingunit 35. Since the pulse width modulation controller unit 30 controlsboth the magnitude and the frequency of the voltage supplied to themotor windings, in a simplified system the voltage control unit 20 maybe dispensed with, whereby the rectification unit 25 may then comprise apassive rectifier.

Referring also to FIG. 2, the microprocessor controls the voltage Vsupplied to a winding and the frequency f at which the supply isswitched on and off in a relationship shown, and which also expressed

V=V0+vf_Ratio*f

where V0 is an initial constant voltage, vf_Ratio (elsewhere indicatedas V:f ratio) is the ratio of voltage over frequency (i.e. Vn/fn).

The motor operates in synchronous mode. The initial voltage setting V0is selected to ensure that there is enough current to generate therequired torque to start-up the motor. Similarly, the slope of the V-frelationship is selected to ensure excess torque is available during thestart-up period and during operation to overcome any transient load thatmay be present while maintaining current below limits.

The motor is operated in synchronous mode using a voltage to frequencyramp which is selected to ensure that optimal excess torque is presentduring the start-up period.

Referring to FIG. 3, the voltage V for full speed operation is set toensure the motor operates in the stable region. Operation at the lefthand side of the minimum current in FIG. 3 makes the motor vulnerable toloss of synchronism under momentary load transients.

The acceleration time (the time it takes the motor to reach fulloperating speed from a stationary position) and thus the accelerationrate is selected to ensure adequate start time within the operationalrequirements of the equipment in the field to preserve the life of theequipment.

It will be seen that providing V0 and vf_Ratio are sufficient, no sensorcircuitry is required.

In a preferred embodiment, the novel method is applied to an electricalsubmersible pump system that includes a motor driving a centrifugal pumpand a power supply cable that can be in excess of 600 m and typically inthe range of 3000 m to 7500 m. As the drives used to control such ESPsystems are typically low voltage, a step-up isolation transformerbetween the drive circuit and the motor is sometimes necessary(represented by Isolation Tx in the embodiment shown in FIG. 5). The useof such devices as isolation transformers makes conventional startup andoperation of motors in such application even harder due to the loss ofphase information across the transformer. The novel method isadvantageously immune to loss of phase information as the current isinherently set by the magnitude of the voltage supply at a givenfrequency.

In contrast to the conventional art, the novel method is fully open loopand does not rely on direct sensing of the motor parameters inoperation, but instead on intimate knowledge of the motorcharacteristics of impedance and back-emf and also on the supply cablecharacteristics, all of which may readily be determined fromspecifications and by conventional measurement techniques in the field,preferably before deployment in the well or other use situation. In thisway the start parameters of the system are established, wherein thestart characteristics comprise an initial voltage and a ramp. Theprincipal parameters required to establish the start characteristics aremotor impedances and back-emf, and cable impedance. The voltage at agiven frequency is set to generate stator currents that are enough togenerate torque for acceleration and load with margin to cater fortransient loads. The initial voltage is set to generate enough currentat standstill to generate enough torque to overcome any bearingfriction. The voltage is set in a predetermined way and programmed intothe drive, and the voltage as a function of frequency is determined fromthe motor and cable characteristics. The equation that governs operationis thus predetermined based on motor and cable characteristics andincorporated into the drive system as a hardware or software component.

At a given frequency or motor speed, the voltage applied to the motoracts against the back-emf generated on the motor at that speed. Theresulting current is a result of the difference between the supplyvoltage and back-emf applied to the impedance of the motor and cable.Therefore, the level of current is set by the level of voltage appliedto the motor. As the level of torque at a given speed is a fixedquantity, the component of the current that would generate the requiredtorque in conjunction with a given back-emf is also fixed. Therefore,the level of voltage supply is important. Too much voltage will generatecurrent in excess with what is required so leading to much reactivepower contributing to the motor heating. Too little voltage will notgenerate the required current so the motor with drop out of step. Sothere is a fine balance to be reached for a given motor/cable system.This balance is achieved by determining the system parameters and thenmaintaining the V:f relationship as set forth herein.

A simplified per-phase equivalent circuit of a motor system is shown inFIG. 5. As stated above, the motor is characterized by its back-emf andits inductance and resistance. The cable is characterised by itsimpedance which is a function of conductor gauge, length and lay-up. Theback-emf E is a function of speed and it is constant at a given speed.The component of current that is in phase with the back emf is thecomponent that generates the torque. The component of the current thatis perpendicular to back-emf generates reactive power which circulates.Some of this current is necessary as it accounts for the reactive dropin the motor and cable inductance and any excess beyond a small amountis only generated as power (I²R) losses and does not contribute totorque generation. It is therefore clear that the supply voltage has tobe selected to within a narrow range to supply the torque, the reactivedrop and a small margin to cover for increased torque required duringtransients.

Based on the equivalent circuit (FIG. 5), it is possible to determinethe characteristics of the motor current as a function of voltage at agiven supply frequency i.e. motor speed. As illustrated in FIG. 3, for agiven frequency supply, the phase rms current as a function of supplyvoltage follows a square law with a minimum current encountered at aspecific voltage level.

This is due to the complex nature of what is taking place within themachine. The motor and associated cables are characterized by a compleximpedance made out by the resistance and inductance. For a givenfrequency this quantity is constant: Z=R+jwL. Simply put the current is:I=(V-E)/Z, all of these being vectorial or complex quantities. It is thevectorial difference between the supply voltage and back-emf that drivesthe current.

The other fixed quantity is the back-emf of the motor as it isproportional to speed. The current magnitude and angular relationship tothe supply voltage V and back-emf E (FIG. 5) are all dependent of themagnitude of the voltage V applied at a given frequency. The realcomponent of the current Isupply is fixed and driven by the torquerequired to drive the load at that given frequency. There are voltagesupply conditions where the phase relationship between V and E result inincreasing current while the supply voltage is reduced.

In a preferred embodiment, the load is a centrifugal pump withcharacteristics where the load torque is the square of the speed and thepower is cubic law of the speed. The permanent magnet synchronousmachine is capable of developing constant torque when supplied withconstant current at any speed. Due to this characteristics, permanentmagnet synchronous machines are well suited to accelerate load withsquare law as a function of speed.

It is clear that at the right hand side of the motor current:supplyvoltage (I:V) curve of FIG. 3, the motor is inherently stable as thevoltage supply is adequate to supply the required current. However, itis clear also that going up the curve is not necessary as it generatemore current than required without additional benefits. Operating atclose proximity to the minimum under all operating conditions is optimalfor system operation and efficiency.

FIG. 4 shows a plurality of I:V curves, each representing a differentfrequency in the frequency range of the supply to the motor,corresponding to the speed range of the motor, wherein the locus of therespective optimal operating points of each of the I:V curves isrepresented by the broken line.

The voltage:frequency (V:f) ratio, represented in FIG. 2, may be asingle value or may be a piecewise linear function. The single value tobe used is selected based on the location of the locus of the minimumcurrents (FIG. 4). This value needs to ensure that at any frequencypoint between the start frequency and the end frequency, the operatingpoint is always at least slightly at the right hand side of the locus asshown in FIG. 4 and hence in the region of stable operation of themotor.

The V:f ratio is a constant quantity that is derived from the requiredacceleration of the system balanced by the need to cool the motor. Asthe cooling to the motor is provided by the pumped fluid, theacceleration and current levels must be balanced to ensure that thepumped fluid can cool the amount of losses generated during accelerationperiod.

The equation can be stated as:

V[supplied to winding]=C1+C2*f

wherein both C1 and C2 are constants

C2 is the ratio of Vn and fn (FIG. 2) where Vn is nominal root meansquare (RMS) voltage at nominal speed and fn is the supply frequency atnominal speed.

Supply frequency is stated in Hz and is related to speed and motor polepairs as follows:

f=(rpm*Pole_Pairs)/60

The invention may advantageously be employed in ESP systems withsynchronous permanent magnet motors, particularly those that have acable length in excess of 50 m and that are supplied either directlyfrom the drive or through a step-up transformer. In particular, it mayadvantageously be used for ESP systems wherein the motor is connected toa centrifugal pump.

The initial voltage (V0) is applied when the motor is at standstill orstatic condition. The current that results for this initial voltage isonly limited by the resistance of the winding and the cable. Typically,an initial voltage is selected that would result in about 30% of ratedcurrent at start-up to overcome any stiction or friction. The initialvoltage may be calculated by multiplying the desired current by the lineresistance of the motor and its associated cable.

The curve is dependent on the load conditions, whereby a set of I:Vcurves can be generated in accordance with the conventional art that arerelated to the load at a given frequency. The start characteristics areselected for the full load condition of the motor, so that the I:V curvewill guarantee that the motor will start at any load condition. Thisprovides a single characteristic that will accommodate steady-state aswell as system transients.

The initial voltage (V0) inherently adds to the voltage margin to allowfor acceleration and transients at start-up or at low speed. However, asthe speed increases this effect of the initial voltage value reduces,and so allowance is made for the required acceleration and transientswithin the V:f ratio and the associated margin obtained from the I:Vcurves.

Although in theory one could experimentally deduce a working V:f ratio,in practice the open loop nature of the controls would make it veryhazardous to specify control system parameters in this way. Inaccordance with the novel method, the system hardware parametersincluding the motor and cable characteristics reflecting in particularthe cable length are measured and analysed so as to obtain the requiredoperating profiles and the optimal operating conditions withoutexperimentation.

This is important, particularly since hydrocarbon extraction is capitalintensive and it is undesirable to spend time tuning the motor controlsystem while the motor is deployed in the well.

The desired acceleration rate to suit the operating conditions of thesystem can be obtained by selecting an appropriate V:f ratio (FIG. 2),whereby current is supplied to compensate for the acceleration torque inaccordance with the known relationship: J·dw/dt.

The acceleration rate is dictated by the difference between theelectromagnetic torque generated at the motor shaft and the load torque(comprising pump load, friction and any other losses). This differencedrives the J·dw/dt thus the dw/dt or acceleration. In the novel method,the rate of acceleration is determined by the rate at which the voltageis varied as a function of time. As the electromagnetic torque isdictated by the supplied current which in turn is a result of appliedvoltage, it is possible to ensure sufficient current to maintain thedesired acceleration by selecting a V:f ratio that is consistent withthe required acceleration rate.

A simple example is as follows:

For a given frequency the voltage is fixed by the vf ratio:

V=V0+vf*f

Supply frequency as a function of time at given acceleration rate isdefined as:

f=Acceleration Rate*time

Therefore, the supply voltage is: V=V0+vf*Accel*time

wherein Accel is Acceleration rate, and

Total torque(f)=Load Torque(f)+Inertia*Accel

The required torque at a given speed is augmented by providing theacceleration torque to be approximately proportional to the accelerationrate.

A faster acceleration rate may therefore be obtained by increasing theV:f ratio as required by the operating conditions of the system.

The novel method may be applied to all synchronous motors with permanentmagnet excitation or current excitation. For permanent magnet motors itmay be applied to both brushless-DC motors (motors with trapezoidalback-emf) and brushless-AC motors (motors with sinewave back-emf).

It will be appreciated that the foregoing example applies equally to theembodiment set forth above, whereby a method of controlling an electricpower supply to a synchronous permanent magnet motor driving a load andhaving a plurality of windings, each winding being supplied with powerat a root mean square supply voltage V3 and a supply frequency via arespective conductor, so as to accelerate the motor through a range ofspeed from rest, comprises determining system parameters includingcharacteristics of the load, the impedance and back-emf of the motor andthe impedance of each of the conductors; determining based on saidsystem parameters a root mean square first voltage V0 at which thesupply generates torque in the motor at rest sufficient to start themotor in rotation; determining based on said system parameters a ratiobetween the supply voltage V3 and supply frequency, wherein the ratiodefines, for each of a range of supply frequencies corresponding to therange of speed of the rotating motor, a root mean square second voltageV2 at which current flowing through each winding increases with bothincrease and decrease in voltage, and V2>V0; supplying power to eachwinding at the first voltage V0 so as to start the motor from rest; andprogressively increasing both the supply voltage and the supplyfrequency while maintaining the supply voltage V3 with respect to supplyfrequency at a value sufficiently in excess of V2 to ensure stableoperation of the motor until the motor has reached a desired operatingspeed; wherein the said ratio between the supply voltage V3 and supplyfrequency is determined based on said system parameters to provide adesired rate of acceleration determined by the supply voltage.

Preferably the supply voltage V3 is maintained with respect to supplyfrequency at a value just sufficiently above V2 to ensure stableoperation, whereby V3<1.3*V2, more preferably V3<1.2*V2, still morepreferably V3<1.1*V2, although these values may be modified in practiceto reflect the desired acceleration rate and system parameters (e.g.transient loads resulting from impure wellbore fluids or the like) ofany given installation.

The first voltage V0 is preferably determined as that voltage at whichthe supply generates torque in the motor at rest slightly in excess ofthat required to overcome starting loads, for example, not more than130%, more preferably not more than 120%, still more preferably not morethan about 110% of that voltage at which the supply is calculated basedon the system parameters to generate torque in the motor at rest justsufficient to start the motor in rotation.

In summary, a preferred embodiment provides a synchronous permanentmagnet motor which is controlled independently of position sensing meansby determining the system parameters including the motor impedance andback-emf and the cable impedance and supplying power according to apredefined voltage:frequency ratio which is determined based on saidsystem parameters to provide a desired rate of acceleration determinedby the supply voltage.

What is claimed is:
 1. A method of controlling an electric power supplyelectrically connected to a synchronous permanent magnet motor having aplurality of windings comprising: supplying each of the plurality ofwindings of the synchronous permanent magnet motor with a root meansquare supply voltage applied at a supply frequency via an electricalconductor in a wellbore, wherein the root mean square supply voltage isdetermined from an initial constant voltage, a constant ratio of voltageover frequency, and the supply frequency; and determining, prior tosupplying each of the plurality of windings with the root mean squaresupply voltage applied at the supply frequency, the initial constantvoltage from one or more characteristics of the synchronous permanentmagnet motor and one or more characteristics of the electricalconductor, wherein the initial constant voltage is a predetermined valuethat supplies a current to generate a torque that turns the motor from astationary position, wherein the constant ratio of voltage overfrequency is used to operate the synchronous permanent magnet motor fora start-up period and an operation period without regard to a motorload, and wherein the electric power supply is controlled withoutfeedback from a rotor position signal.
 2. The method of claim 1, furthercomprising determining the constant ratio of voltage over frequency bydetermining a minimum current value for each frequency within a range ofsupply frequencies that are associated with a range of speeds for thesynchronous permanent magnet motor, wherein the minimum current valuefor each frequency within the range of supply frequencies corresponds toa locus on a current:voltage curve.
 3. The method of claim 1, furthercomprising determining, prior to supplying each winding with the rootmean square supply voltage applied at the supply frequency, the constantratio of voltage over frequency from the one or more characteristics ofthe synchronous permanent magnet motor and the one or morecharacteristics of the respective conductor that supplies the root meansquare supply voltage to the synchronous permanent magnet motor.
 4. Themethod of claim 1, wherein the synchronous permanent magnet motor isarranged to drive an electric submersible pump, wherein the one or morecharacteristics of the respective conductor used to determine theinitial constant voltage V0 comprises an impedance of the respectiveconductor, and wherein the impedance of the respective conductor isdetermined from a length of the respective conductor.
 5. The method ofclaim 1, wherein the one or more characteristics of the synchronouspermanent magnet motor used to determine the initial constant voltage isselected from the group consisting of: a back-emf of the synchronouspermanent magnet; an inductance of the synchronous permanent magnetmotor; and a resistance of the synchronous permanent magnet motor. 6.The method of claim 1, wherein the supply frequency is determined from aspeed of the synchronous permanent magnet motor and the motor pole pairsof the synchronous permanent magnet motor.
 7. A method of controlling anelectric power supply to a synchronous permanent magnet motor,comprising: determining a plurality of system parameters; determiningaccording to the system parameters a root mean square first voltagesupplied by the electric power supply that starts the synchronouspermanent magnet motor in rotation; determining based on the systemparameters a ratio between the supply voltage and the supply frequency,wherein the ratio defines, for each of a range of supply frequenciescorresponding to a range of speed, a root mean square second voltage atwhich a current flowing through each of a plurality of windings of thesynchronous permanent magnet motor increases with an increase in avoltage corresponding to the root mean square second voltage; supplyingpower to each of the plurality of windings of the synchronous permanentmagnet motor at the root mean square first voltage to start thesynchronous permanent magnet motor from rest; and increasing both theroot mean square supply voltage and the supply frequency and maintainingthe ratio and delivering the supply voltage at a desired relationship tothe root mean square second voltage until the synchronous permanentmagnet motor has reached a desired operating speed.
 8. The method ofclaim 7, wherein the ratio between the root mean square supply voltageand the supply frequency is determined from the system parameters toprovide a desired rate of acceleration.
 9. The method of claim 7,wherein the root mean square supply voltage is maintained according tothe supply frequency at a value, whereby the root mean square supplyvoltage V3 is less than 1.3*the root mean square second voltage.
 10. Themethod of claim 7, wherein the root mean square supply voltage ismaintained according to the supply frequency at a value whereby the rootmean square supply voltage is less than 1.2*the root mean square secondvoltage.
 11. The method of claim 7, wherein the root mean square supplyvoltage is maintained according to the supply frequency at a valuewhereby the root mean square supply voltage is less than 1.1*the rootmean square second voltage.
 12. The method of claim 7, whereindetermining the plurality of system parameters further comprisesdetermining at least one selected from the group consisting of: acharacteristic of the load; an impedance of the synchronous permanentmagnet motor; a back-emf of the synchronous permanent magnet motor; andan impedance of each of the respective conductors.
 13. The method ofclaim 7, wherein the root mean square first voltage and the ratio aredetermined without sensing a plurality of synchronous permanent magnetmotor parameters during operation.
 14. The method of claim 7, furthercomprising increasing an acceleration rate of the synchronous permanentmagnet motor by increasing the ratio, and wherein the supply frequencyis regulated by a speed of the synchronous permanent magnet motor andthe motor pole pairs of the synchronous permanent magnet motor.
 15. Asystem comprising: a synchronous permanent magnet motor deployed in awellbore and configured to drive a load, the synchronous permanentmagnet motor comprising a plurality of windings; and a control apparatusoperatively coupled to the synchronous permanent magnet motor via one ormore electric cables, wherein the control apparatus is configured to:supply each of the plurality of windings of the synchronous permanentmagnet motor with a root mean square supply voltage V applied at asupply frequency f in determined from an initial constant voltage V0, aconstant ratio of voltage over frequency vf_Ratio, and the supplyfrequency f; determine, prior to supplying each of the plurality ofwindings with the root mean square supply voltage V applied at thesupply frequency f, the initial constant voltage V0 from one or morecharacteristics of the synchronous permanent magnet motor and one ormore characteristics of the corresponding electric cable; and select avalue for the constant ratio of voltage over frequency vf_Ratio thatcompensates for an acceleration torque of the synchronous permanentmagnet motor, wherein the initial constant voltage V0 is selected togenerate a torque that turns the synchronous permanent magnet motor at astandstill state, and wherein the initial constant voltage V0 and theconstant ratio of voltage over frequency vf_Ratio is determined withoutreliance on sensing a plurality of motor parameters corresponding to thesynchronous permanent magnet motor in operation.
 16. The system of claim15, wherein the synchronous permanent magnet motor is configured todrive an electric submersible pump.
 17. The system of claim 15, whereinthe control apparatus is further configured to increase an accelerationrate of the synchronous permanent magnet motor by increasing the valueof the constant ratio of voltage over frequency vf_Ratio.
 18. The systemof claim 15, wherein the selection of the constant ratio of voltage overfrequency vf_Ratio is prior to supplying each winding with the root meansquare supply voltage V applied at the supply frequency f, and whereinthe constant ratio of voltage over frequency vf_Ratio is determined fromthe at least the impedance of the synchronous permanent magnet motor andthe impedance of the corresponding electric cable.
 19. The system ofclaim 15, wherein supplying each winding via the electric cables with aroot mean square supply voltage V applied at a supply frequency f inrelation to an initial constant voltage V0, a constant ratio of voltageover frequency vf_Ratio, and the supply frequency f is based upon theexpression V=V0+vf_Ratio*f.
 20. The system of claim 15, wherein thecontrol apparatus is further configured to determine the initialconstant voltage V0 from at least a back-emf of the synchronouspermanent magnet motor and an inductance of the synchronous permanentmagnet motor.
 21. The system of claim 15, wherein the supply frequency fis related to the speed of the synchronous permanent magnet motor andthe motor pole pairs of the synchronous permanent magnet motor.
 22. Amethod of controlling a synchronous permanent magnet motor comprising:determining a plurality of system parameters; determining based on theplurality of system parameters a ratio between a supply voltage and asupply frequency, wherein the ratio provides a desired rate ofacceleration determined by the supply voltage; supplying power to aplurality of windings at a first voltage to start a rotor from rest; andincreasing the supply voltage and the supply frequency andsimultaneously maintaining the supply voltage at a predeterminedrelationship to a second voltage until the synchronous permanent magnetmotor has reached a desired operating speed, wherein the second voltageis greater than the first voltage and generates an increasing currentwith a decrease in the second voltage, wherein the first voltage and theratio are determined without a reliance on a position sensing of therotor.